Compact contractive projections in continuous function spaces.

Contractive Projections on Banach Spaces

Increasing sequences of contractive projections on a reflexive LP space share an unconditionality property similar to that exhibited sequences of self-adjoint projections on a Hilbert space. A slight variation of this property is shown to be precisely the correct condition on a reflexive Banach space to ensure that every operator with a contractive AC-functional calculus is scalar-type spectraL

Ranges of Positive Contractive Projections in Nakano Spaces

We show that in any nontrivial Nakano space X = Lp(·)(Ω, Σ, μ) with essentially bounded random exponent function p(·), the range Y = R(P ) of a positive contractive projection P is itself representable as a Nakano space LpY (·)(ΩY , ΣY , νY ), for a certain measurable set ΩY ⊆ Ω (the support of the range), a certain sub-sigma ring ΣY ⊆ Σ (with maximal element ΩY ) naturally determined by the la...

On function spaces of Corson-compact spaces

We apply elementary substructures to characterize the space Cp(X) for Corsoncompact spaces. As a result, we prove that a compact space X is Corson-compact, if Cp(X) can be represented as a continuous image of a closed subspace of (Lτ ) × Z, where Z is compact and Lτ denotes the canonical Lindelöf space of cardinality τ with one non-isolated point. This answers a question of Archangelskij [2].

Contractive Projections and Prediction Operators

Characterizing Continuous Functions on Compact Spaces

We consider the following problem: given a set X and a function T : X → X, does there exist a compact Hausdorff topology on X which makes T continuous? We characterize such functions in terms of their orbit structure. Given the generality of the problem, the characterization turns out to be surprisingly simple and elegant. Amongst other results, we also characterize homeomorphisms on compact me...